We address the problem of planning robot motions in constrained configuration spaces where the constraints change throughout the motion. The problem is formulated as a fixed sequence of intersecting manifolds, which the robot needs to traverse in order to solve the task. We specify a class of sequential motion planning problems that fulfill a particular property of the change in the free configuration space when transitioning between manifolds. For this problem class, we develop the algorithm Planning on Sequenced Manifolds (PSM*) which searches for optimal intersection points between manifolds by using RRT* in an inner loop with a novel steering strategy. We provide a theoretical analysis regarding PSM*s probabilistic completeness and asymptotic optimality. Further, we evaluate its planning performance on multi-robot object transportation tasks. Video: https://youtu.be/Q8kbILTRxfU Code: https://github.com/etpr/sequential-manifold-planning

翻译：我们解决了在限制因素在整个运动中变化的有限配置空间内规划机器人运动的问题。 问题被设计成一个固定的交叉点序列, 机器人需要绕过它才能完成这项任务。 我们具体规定了一组顺序运动规划问题, 满足了在多块之间转换时自由配置空间变化的特定属性。 对于这个问题类别, 我们开发了按顺序排列的Manfolds( PSM* ) 算法规划( PSM* ), 通过在新式指导战略的内环中使用 RRT* 来搜索各块之间的最佳交叉点。 我们提供了对 PSM* 概率完整性和无线优化性的理论分析。 此外, 我们还评估了多机器人物体运输任务规划绩效。 视频: https://youtu.be/ Q8kblilTRxfU 代码: https://github. com/etpr/ equegtial-manyfold- plancation。